Consider the following problem: A farmer with 750 ft offencing wants to enclose a rectangular area and then divideit into four pens with fencing parallel to one side of therectangle. What is the largest possible total area of the fourpens?(a) Draw several diagrams illustrating the situation, somewith shallow, wide pens and some with deep, narrowpens. Find the total areas of these configurations. Doesit appear that there is a maximum area? If so, estimate it.(b) Draw a diagram illustrating the general situation. Introducenotation and label the diagram with your symbols.(c) Write an expression for the total area.(d) Use the given information to write an equation thatrelates the variables.(e) Use part (d) to write the total area as a function of onevariable.(f ) Finish solving the problem and compare the answerwith your estimate in part (a).
Consider the following problem: A farmer with 750 ft of
fencing wants to enclose a rectangular area and then divide
it into four pens with fencing parallel to one side of the
rectangle. What is the largest possible total area of the four
pens?
(a) Draw several diagrams illustrating the situation, some
with shallow, wide pens and some with deep, narrow
pens. Find the total areas of these configurations. Does
it appear that there is a maximum area? If so, estimate it.
(b) Draw a diagram illustrating the general situation. Introduce
notation and label the diagram with your symbols.
(c) Write an expression for the total area.
(d) Use the given information to write an equation that
relates the variables.
(e) Use part (d) to write the total area as a function of one
variable.
(f ) Finish solving the problem and compare the answer
with your estimate in part (a).
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